Dynamics and optimal control of a Zika model with sexual and vertical transmissions

A new transmission model of Zika virus with three transmission routes including human transmission by mosquito bites, sexual transmission between males and females and vertical transmission is established. The basic reproduction number $ R_{0} $ is derived. When $ R_{0} < 1 $, it is proved that the disease-free equilibrium is globally stable. Furthermore, the optimal control and mitigation methods for transmission of Zika virus are deduced and explored. The MCMC method is used to estimate the parameters and the reasons for the deviation between the actual infection cases and the simulated data are discussed. In addition, different strategies for controlling the spread of Zika virus are simulated and studied. The combination of mosquito control strategies and internal human control strategies is the most effective way in reducing the risk of Zika virus infection.